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Author: Linda Hackenbruck Publisher: Outskirts Press ISBN: 1977279171 Category : Religion Languages : en Pages : 174
Book Description
In a world turning from God, how do you prove Him? Are there times in your life when you want to share your love of God and His reality, but you don’t know how? How can you do so in a loving, non-threatening way? In Powerful Proof, Linda Hackenbruck shares with you her personal stories of God’s love and transforming power; stories she shares when asked why she lives for God. They span decades of loving and living for Him and are filled with His miracles. Throughout her life, God stayed with her, as her confidant, comforting her in trials and answering her simple prayers in unexpected ways. His deep love led her through pain and suffering, harm to her infant daughter and the death of her son. As she was broken and emptied of herself, God changed her for His purposes and use in His kingdom, finally filling her with unbelievable joy. The following are glimpses into what He has done: *How He used a broken tail light to save her son from continuing down a dark path. *How He saved her infant daughter’s life after autopsy papers and a burial outfit had been requested *How, after three years of trying to forgive the doctor who had hurt her baby, God completed her forgiveness in the most unlikely way. *How, after decades of prayer, her father experienced two miracles and came to know God as personal and loving. *How He delivered a new dishwasher to her front door, even though she had “given up” dishwashers. *How her young daughter prayed for a Christmas pageant dress and it arrived in a paper bag, on the front porch, two days before the pageant. *How He saved her husband from stage 4 cancer through prayer and His intervention. Linda will share truths she has learned in her lifetime of trusting God: *He is always trustworthy. *Giving up your will in obedience to His brings abundant blessing. *You can trust Him with your children, whether He miraculously saves them or shocks you by taking them home to Himself. *He always hears our prayers and answers them in His time and in unexpected ways. *He talks directly to us in ways we can understand. *He is able to heal us physically and emotionally. *He loves an honest and humble heart. *He can take our anger and pain and turn them to joy. *If we ask, He will give us wisdom in our life situations. *We can’t out love God. Our world is working hard to make Jesus, God and the Holy Spirit irrelevant and foolish. Many people struggle with believing in Them. When asked why she lives for God and can be so sure He is real, Linda tells them God is not only real but is lovingly involved in her everyday life. She shares her stories and people listen, because they are stories of God in action. They are stories of a God they can relate to and a God they can believe in. They are her absolute truth as she has lived it. She joyfully shares them with you.
Author: Linda Hackenbruck Publisher: Outskirts Press ISBN: 1977279171 Category : Religion Languages : en Pages : 174
Book Description
In a world turning from God, how do you prove Him? Are there times in your life when you want to share your love of God and His reality, but you don’t know how? How can you do so in a loving, non-threatening way? In Powerful Proof, Linda Hackenbruck shares with you her personal stories of God’s love and transforming power; stories she shares when asked why she lives for God. They span decades of loving and living for Him and are filled with His miracles. Throughout her life, God stayed with her, as her confidant, comforting her in trials and answering her simple prayers in unexpected ways. His deep love led her through pain and suffering, harm to her infant daughter and the death of her son. As she was broken and emptied of herself, God changed her for His purposes and use in His kingdom, finally filling her with unbelievable joy. The following are glimpses into what He has done: *How He used a broken tail light to save her son from continuing down a dark path. *How He saved her infant daughter’s life after autopsy papers and a burial outfit had been requested *How, after three years of trying to forgive the doctor who had hurt her baby, God completed her forgiveness in the most unlikely way. *How, after decades of prayer, her father experienced two miracles and came to know God as personal and loving. *How He delivered a new dishwasher to her front door, even though she had “given up” dishwashers. *How her young daughter prayed for a Christmas pageant dress and it arrived in a paper bag, on the front porch, two days before the pageant. *How He saved her husband from stage 4 cancer through prayer and His intervention. Linda will share truths she has learned in her lifetime of trusting God: *He is always trustworthy. *Giving up your will in obedience to His brings abundant blessing. *You can trust Him with your children, whether He miraculously saves them or shocks you by taking them home to Himself. *He always hears our prayers and answers them in His time and in unexpected ways. *He talks directly to us in ways we can understand. *He is able to heal us physically and emotionally. *He loves an honest and humble heart. *He can take our anger and pain and turn them to joy. *If we ask, He will give us wisdom in our life situations. *We can’t out love God. Our world is working hard to make Jesus, God and the Holy Spirit irrelevant and foolish. Many people struggle with believing in Them. When asked why she lives for God and can be so sure He is real, Linda tells them God is not only real but is lovingly involved in her everyday life. She shares her stories and people listen, because they are stories of God in action. They are stories of a God they can relate to and a God they can believe in. They are her absolute truth as she has lived it. She joyfully shares them with you.
Author: Martin Aigner Publisher: Springer Science & Business Media ISBN: 3662223430 Category : Mathematics Languages : en Pages : 194
Book Description
According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
Author: Richard H. Hammack Publisher: ISBN: 9780989472111 Category : Mathematics Languages : en Pages : 314
Book Description
This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.
Author: Daniel J. Velleman Publisher: Cambridge University Press ISBN: 0521861241 Category : Mathematics Languages : en Pages : 401
Book Description
Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.
Author: Titu Andreescu Publisher: ISBN: 9780996874595 Category : Induction (Mathematics) Languages : en Pages : 432
Book Description
This book serves as a very good resource and teaching material for anyone who wants to discover the beauty of Induction and its applications, from novice mathematicians to Olympiad-driven students and professors teaching undergraduate courses. The authors explore 10 different areas of mathematics, including topics that are not usually discussed in an Olympiad-oriented book on the subject. Induction is one of the most important techniques used in competitions and its applications permeate almost every area of mathematics.
Author: Ethan D. Bloch Publisher: Springer Science & Business Media ISBN: 1441971270 Category : Mathematics Languages : en Pages : 378
Book Description
“Proofs and Fundamentals: A First Course in Abstract Mathematics” 2nd edition is designed as a "transition" course to introduce undergraduates to the writing of rigorous mathematical proofs, and to such fundamental mathematical ideas as sets, functions, relations, and cardinality. The text serves as a bridge between computational courses such as calculus, and more theoretical, proofs-oriented courses such as linear algebra, abstract algebra and real analysis. This 3-part work carefully balances Proofs, Fundamentals, and Extras. Part 1 presents logic and basic proof techniques; Part 2 thoroughly covers fundamental material such as sets, functions and relations; and Part 3 introduces a variety of extra topics such as groups, combinatorics and sequences. A gentle, friendly style is used, in which motivation and informal discussion play a key role, and yet high standards in rigor and in writing are never compromised. New to the second edition: 1) A new section about the foundations of set theory has been added at the end of the chapter about sets. This section includes a very informal discussion of the Zermelo– Fraenkel Axioms for set theory. We do not make use of these axioms subsequently in the text, but it is valuable for any mathematician to be aware that an axiomatic basis for set theory exists. Also included in this new section is a slightly expanded discussion of the Axiom of Choice, and new discussion of Zorn's Lemma, which is used later in the text. 2) The chapter about the cardinality of sets has been rearranged and expanded. There is a new section at the start of the chapter that summarizes various properties of the set of natural numbers; these properties play important roles subsequently in the chapter. The sections on induction and recursion have been slightly expanded, and have been relocated to an earlier place in the chapter (following the new section), both because they are more concrete than the material found in the other sections of the chapter, and because ideas from the sections on induction and recursion are used in the other sections. Next comes the section on the cardinality of sets (which was originally the first section of the chapter); this section gained proofs of the Schroeder–Bernstein theorem and the Trichotomy Law for Sets, and lost most of the material about finite and countable sets, which has now been moved to a new section devoted to those two types of sets. The chapter concludes with the section on the cardinality of the number systems. 3) The chapter on the construction of the natural numbers, integers and rational numbers from the Peano Postulates was removed entirely. That material was originally included to provide the needed background about the number systems, particularly for the discussion of the cardinality of sets, but it was always somewhat out of place given the level and scope of this text. The background material about the natural numbers needed for the cardinality of sets has now been summarized in a new section at the start of that chapter, making the chapter both self-contained and more accessible than it previously was. 4) The section on families of sets has been thoroughly revised, with the focus being on families of sets in general, not necessarily thought of as indexed. 5) A new section about the convergence of sequences has been added to the chapter on selected topics. This new section, which treats a topic from real analysis, adds some diversity to the chapter, which had hitherto contained selected topics of only an algebraic or combinatorial nature. 6) A new section called ``You Are the Professor'' has been added to the end of the last chapter. This new section, which includes a number of attempted proofs taken from actual homework exercises submitted by students, offers the reader the opportunity to solidify her facility for writing proofs by critiquing these submissions as if she were the instructor for the course. 7) All known errors have been corrected. 8) Many minor adjustments of wording have been made throughout the text, with the hope of improving the exposition.
Author: Nathan Schneider Publisher: Univ of California Press ISBN: 0520269071 Category : Religion Languages : en Pages : 268
Book Description
In this tour of the history of arguments for and against the existence of God, Nathan Schneider embarks on a remarkable intellectual, historical, and theological journey through the centuries of believers and unbelieversÑfrom ancient Greeks, to medieval Arabs, to todayÕs most eminent philosophers and the New Atheists. Framed by an account of SchneiderÕs own unique journey, God in Proof illuminates the great minds who wrestled with one of historyÕs biggest questions together with their arguments, bringing them to life in their time, and our own. SchneiderÕs sure-handed portrayal of the characters and ideas involved in the search for proof challenges how we normally think about doubt and faith while showing that, in their quest for certainty and the proofs to declare it, thinkers on either side of the God divide are often closer to one another than they would like to think.
Author: Morten Heine Sørensen Publisher: Elsevier ISBN: 0080478921 Category : Mathematics Languages : en Pages : 457
Book Description
The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance,minimal propositional logic corresponds to simply typed lambda-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic types, sequent calculus is related to explicit substitution, etc.The isomorphism has many aspects, even at the syntactic level:formulas correspond to types, proofs correspond to terms, provability corresponds to inhabitation, proof normalization corresponds to term reduction, etc.But there is more to the isomorphism than this. For instance, it is an old idea---due to Brouwer, Kolmogorov, and Heyting---that a constructive proof of an implication is a procedure that transformsproofs of the antecedent into proofs of the succedent; the Curry-Howard isomorphism gives syntactic representations of such procedures. The Curry-Howard isomorphism also provides theoretical foundations for many modern proof-assistant systems (e.g. Coq).This book give an introduction to parts of proof theory and related aspects of type theory relevant for the Curry-Howard isomorphism. It can serve as an introduction to any or both of typed lambda-calculus and intuitionistic logic.Key features- The Curry-Howard Isomorphism treated as common theme- Reader-friendly introduction to two complementary subjects: Lambda-calculus and constructive logics- Thorough study of the connection between calculi and logics- Elaborate study of classical logics and control operators- Account of dialogue games for classical and intuitionistic logic- Theoretical foundations of computer-assisted reasoning· The Curry-Howard Isomorphism treated as the common theme.· Reader-friendly introduction to two complementary subjects: lambda-calculus and constructive logics · Thorough study of the connection between calculi and logics.· Elaborate study of classical logics and control operators.· Account of dialogue games for classical and intuitionistic logic.· Theoretical foundations of computer-assisted reasoning
Author: Jia Jiang Publisher: Harmony ISBN: 0804141398 Category : Business & Economics Languages : en Pages : 242
Book Description
The inspiring, relatable, and sometimes outrageous true story of how one man used 100 days of rejection therapy to overcome fear and dare to live more boldly “Rejection Proof smashes fear in the face with a one-two punch. You’ll laugh out loud at Jia’s crazy social experiments, but you’ll also go away thinking differently about what you can accomplish.”—Chris Guillebeau, New York Times bestselling author of The Happiness Pursuit Jia Jiang’s TEDx Talk, “What I learned from 100 days of rejection,” has amassed over ten million views! Jia Jiang came to the United States with the dream of being the next Bill Gates. But despite early success in the corporate world, his first attempt to pursue his entrepreneurial dream ended in rejection. Jia was crushed and spiraled into a period of deep self-doubt. Jia realized that his fear of rejection was a bigger obstacle than any single rejection would ever be; he needed to find a way to cope with being told “no” that wouldn’t destroy him. Inspired by rejection therapy, which uses similar modalities as exposure therapy to desensitize you to the effects of being rejected, he undertook the “100 days of rejection” experiment, during which he willfully sought out rejection on a daily basis—from requesting a lesson in sales from a car salesman (no) to asking a flight attendant if he could make an announcement on the loud speaker (yes) to his famous request to get Krispy Kreme donuts in the shape of Olympic rings (yes, with a viral video to prove it). Over the course of one hundred rejection attempts, Jia realized that even the most preposterous wish might be granted if you ask the right way. He learned the secrets to making successful requests, tactics for picking the right people to approach at the right time, and strategies for converting an initial no into something positive. More important, Jia discovered ways to steel himself against rejection and live more fearlessly—skills that can’t be derailed by a single setback. The changes Jia experienced from his rejection therapy experiment went far beyond becoming more successful in business; he realized that he could apply these techniques to get more out of his relationships with friends, family, and even casual encounters with strangers. Filled with great stories and valuable insight, Rejection Proof shares the secrets of Jia’s rejection journey, distilling each lesson into a strategy that can be used in any negotiation or pitch.
Author: Craig L. Blomberg Publisher: B&H Publishing Group ISBN: 1433691701 Category : Religion Languages : en Pages : 809
Book Description
Questions about the reliability of the New Testament are commonly raised today both by biblical scholars and popular media. Drawing on decades of research, Craig Blomberg addresses all of the major objections to the historicity of the New Testament in one comprehensive volume. Topics addressed include the formation of the Gospels, the transmission of the text, the formation of the canon, alleged contradictions, the relationship between Jesus and Paul, supposed Pauline forgeries, other gospels, miracles, and many more. Historical corroborations of details from all parts of the New Testament are also presented throughout. The Historical Reliability of the New Testament marshals the latest scholarship in responding to New Testament objections, while remaining accessible to non-specialists.
Author: Linda Hackenbruck
Author: Linda Hackenbruck
Author: Martin Aigner
Author: Richard H. Hammack
Author: Daniel J. Velleman
Author: Titu Andreescu
Author: Ethan D. Bloch
Author: Nathan Schneider
Author: Morten Heine Sørensen
Author: Jia Jiang
Author: Craig L. Blomberg